In a triangle the measure of the first angle is three times the measure of the second angle. the measure of the third angle is 60 degrees more than the measure of the second angle. use the fact that the sum of the measures of the three angles of a triangle is 180 degrees to find the measure of each angle

First: 72

Second: 24

Third: 84

Step-by-step explanation:

Let's say that the second angle, the smallest one, is x. Using the provided information, we can make the equation 180=3x+x+x+60, or 180=5x+60. To solve for the second angle, first subtract 60 from each side (120=5x) and then divide each side by five (24=x). Now, to find the first angle, we multiply the second by three (3*24=72). To find the third, add 60 to the second (24+60=84).

b

step-by-step explanation:

b

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)